Connected ICN-(OZ)-PVG-(NZ)-AKL on the 5th and followed signs for the LH/LX/VS/NZ airside connection. Got to row of 5 desks with one monitor displaying the NZ logo (all others off) and agent said "Lufthansa and Swiss only" despite the NZ sign over her head. Would not budge and help us with NZ, so off to immigration. 30+ minute wait in immigration line, officer made me step aside to wait for a supervisor, and then let through. Out to check-in desk and right back through immigration, then up to the gate 77 lounge... good thing I booked a 3.5h layover.